Manometers, barometers: Question bank — Hinglish deep dive

2.2.8 · D5 · Physics › Fluid Mechanics › Manometers, barometers

Definition Is page pe use hone wale symbols (pehle yeh seekho)

$ρ$ (Greek "rho") = fluid ki density, matlab unit volume mein kitna mass packed hai (kg per cubic metre). Mercury jaisi bhaari fluids ka $ρ$ bada hota hai; dekho Density and Specific Gravity.
$g$ = gravitational acceleration, gravity kitni zyada har kilogram ko neeche kheenchti hai ( $\approx 9.8 m/s^{2}$ Earth pe). Yeh decide karta hai ki fluid ke column ka weight kitna hoga.
$h$ = fluid column ki vertical height ya do surfaces ke beech ka vertical gap (metres). Sirf vertical count hota hai — tedi length nahi.
$P_{a t m}$ = atmospheric (air) pressure jo kisi bhi open surface pe push karta hai ( $\approx 1.013 \times 1 0^{5} Pa$ ); dekho Atmospheric Pressure.
$P_{g a s}$ = us trapped gas ya vessel ka pressure jo manometer measure kar raha hai.
$P_{ab s}$ = absolute pressure (true vacuum se measure kiya hua); $P_{g a ug e} = P_{ab s} - P_{a t m}$ = tum atmosphere se kitne upar ho.

Shuru karne se pehle teen anchors yaad rakho:

Sirf vertical height count hoti hai — fluid ka sideways travel free hai.
Same connected fluid, same level ⇒ same pressure (from Pascal's Law).
Barometer ka top vacuum (absolute) hai; open manometer ka arm air (gauge) se milta hai.

Spot the error

"Tank ke bottom pe pressure depend karta hai ki usme kitna paani hai, toh bada tank matlab zyada bottom pressure."

Error: pressure depend karta hai depth

h

pe, total volume pe nahi. Same depth tak bhare do tanks ka bottom pressure equal hoga, chahe width ya total water kuch bhi ho (barometer figure s01 wali same reasoning).

3 0^{\circ}

pe liquid length

L = 0.20 m

wale inclined manometer ke liye,

ρ g h

mein

h = 0.20 m

use karo."

Error: sirf vertical rise gravity ke against push karta hai (staircase figure s02). Use karo

h = L sin θ = 0.20 \times 0.5 = 0.10 m

"Barometer aur open manometer dono

ρ g h

use karte hain, toh dono absolute pressure dete hain."

Error: har column ka top alag hota hai (figure s01 ke dono halves compare karo). Barometer ka top vacuum hai ⇒ absolute; open manometer ka doosra arm

P_{a t m}

pe baithta hai ⇒ uska

ρ g h

sirf gauge (difference) pressure hai.

"Gas pressure padhne ke liye, U-tube ke dono arms mein liquid ki height add karo."

Error: jo matter karta hai woh do free surfaces ke beech ka difference hai (figure s03 mein gap

h

), sum nahi. Shared lower fluid cancel ho jaata hai jab tum reference level pe pressures equate karte ho.

"Kyunki pressure sabhi directions mein push karta hai, horizontal pressure differences bhi manometer fluid ko lift karte hain."

Error: sirf vertical pressure change

ρ g h

gravity ke against mechanical work karta hai; ek horizontal level ke along pressure dono sides pe equal hota hai aur cancel ho jaata hai (figure s02 mein green segments).

"Vacuum ka pressure negative hota hai, toh barometer ka top mercury ko upar kheenchta hai."

Error: vacuum pressure

\approx 0

hota hai, negative nahi. Mercury neeche se

P_{a t m}

ke zariye open dish pe push hota hai upar (figure s01 mein upward arrow dekho), upar se pull nahi hota.

Why questions

Hydrostatic derivation mein cross-sectional area

A

kyun cancel ho jaata hai?

Kyunki pressure force per area hai: fluid ka extra weight (

\propto A

) equally bade area (

\propto A

) pe baithta hai, toh unka ratio — pressure — area-independent hai.

Barometer mein water ki jagah mercury kyun prefer kiya jaata hai?

Mercury

13.6 \times

zyada dense hai, toh

h = P / ρ g

se column

13.6 \times

chhota hota hai —

\sim 10.3 m

ki jagah

0.76 m

, jo ek bench pe fit ho jaata hai (dekho Density and Specific Gravity).

Unke pressures equate karne ke liye barometer/dish ke do points same horizontal level pe kyun hone chahiye?

Ek connected still fluid mein, equal height pe pressure difference sideways flow drive karta; equilibrium flow forbid karta hai, toh equal level ⇒ equal pressure (Pascal's Law).

Open-tube manometer gauge kyun padhta hai, absolute kyun nahi?

Ek arm

P_{a t m}

ke saath exposed hoti hai, toh height difference measure karta hai ki gas atmosphere se kitna zyada ya kam hai — yeh difference definition se gauge pressure hai.

ρ g h

mein sirf vertical height kyun aata hai, path length kyun nahi?

Kyunki pressure change woh work hai jo gravity fluid pe per unit volume karta hai jab fluid move karta hai; horizontal moves constant gravitational potential pe hote hain (koi work nahi), toh sirf vertical drop count karta hai — exactly staircase figure s02 mein green-vs-red split.

Fast-flowing fluid ke liye tube mein directly

ρ g h

kyun use nahi kar sakte?

ρ g h

static equilibrium (no motion) assume karta hai. Moving fluid mein kinetic-energy terms hote hain jo Bernoulli's Equation handle karta hai.

Barometer atmospheric pressure measure karta hai lekin diver ke kaan ka dard water pressure — same law use karke — kyun?

Dono same free surface se

ρ g h

hain; barometer ki "depth" ek mercury column hai jo air ko balance karta hai, diver ki water depth hai — same physics of weight-per-area from Atmospheric Pressure.

Accelerating manometer ki fluid surface kyun tilt hoti hai?

Kyunki fluid ke frame mein effective gravity real gravity (down) aur inertial "pull" (

- a

) ka vector sum hai, toh free surface khud ko us tilt hue total force ke perpendicular set kar leti hai — surface hamesha effective gravity ke relative flat hoti hai, ground ke relative nahi.

Edge cases

Open manometer tab kya read karta hai jab

P_{g a s} = P_{a t m}

exactly ho?

h = 0

: dono surfaces level hain (figure s03 ka middle), toh gauge pressure zero hai aur device koi height difference nahi dikhata.

Agar barometer ke sealed top mein leak ho jaaye aur air andar aaye toh mercury ka kya hoga?

Trapped air upar pressure add karta hai, toh column girta hai; yeh ab

P_{a t m}

nahi read karta kyunki top ab vacuum nahi raha.

Agar manometer zero absolute pressure (vacuum vessel) wali gas ke saath use ho toh

h

kya hoga?

P_{g a s} = 0

se gauge

= - P_{a t m}

milta hai, toh open arm

h = P_{a t m} / (ρ g)

se girta hai — yeh maximum hai jitna atmosphere us side ko depress kar sakta hai. Yeh barometer jaisa behave karta hai.

Kya water manometer normal-sized lab tube mein

1 atm

ka pressure difference measure kar sakta hai?

Practically nahi — iske liye

\sim 10.3 m

vertical water chahiye. Exactly isliye bade pressures mercury jaisi dense fluids use karte hain.

Do connected arms mein alag liquids hain (oil over water). Kya same-level-same-pressure rule boundary ke across abhi bhi sach hai?

Sirf ek continuous fluid ke andar. Ek interface ke across tumhe har fluid ka apna

ρ g h

account karna hoga; equal pressure shared interface level pe hold karta hai, alag densities ke across blindly nahi.

Air ke saath open liquid surface pe gauge pressure kya hai?

Zero. Gauge

P_{a t m}

ke relative measure kiya jaata hai, aur free surface

P_{a t m}

pe baithti hai, toh

P_{g a ug e} = ρ g (0) = 0

Mountain top pe jahan

P_{a t m}

kam hai, same gas ke liye same manometer bada ya chhota

h

dega?

Bada gauge height:

h = (P_{g a s} - P_{a t m}) / (ρ g)

badhta hai jab

P_{a t m}

girta hai — gas ab us thinner air se zyada exceed karta hai.

Ek sealed barometer lift mein upar ki taraf

a

se accelerate kar raha hai. Mercury column rise karega ya fall?

Yeh chhota hoga. Effective gravity

g + a

ho jaata hai, toh mercury ka har mm bhaari ho jaata hai; lekin air jise yeh balance karta hai woh bhi bhaari hai — same

P_{a t m}

measure karne wale barometer ke liye,

h = P_{a t m} / (ρ (g + a))

actually chhota hota hai. (Dhyan rakho kaunsi quantity fixed hai.)

Free fall mein U-tube manometer (

g_{eff} = 0

) — kya read karta hai?

Kuch meaningful nahi: jab koi effective gravity nahi toh koi

ρ g h

term nahi, toh koi bhi height difference ab pressure se correspond nahi karta — device kaam karna band kar deta hai.

Connections — har linked idea in traps mein kaise fit hoti hai

Parent: Manometers & Barometers — full derivations jin par yeh traps test karte hain.

Question bank — Manometers, barometers

True or false — justify